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2. Copyright©1999 Lynda Greene
Polynomial Multiplication
Copyright©1999 Lynda Greene

3. The FOIL Multiplication Method

4. multiply two binomials, such as: (x + 3)(x - 2)
FOIL is a method used to
multiply two binomials, such as:
(x + 3)(x - 2)
binomial: two terms
Foil has only one use, if there are more than two terms a different method must be used.
Example: (x - 2)(x2 + 2x -3) cannot use FOIL
Three terms: Trinomial

5. (x + y)(a - 2b) FOIL is an acronym, meaning
each letter stands for a word.
O: stands for the outer terms
F: stands for the First terms
(x + y)(a - 2b)
L: stands for the last terms
I: stands for the inner terms

6. - 2bx ax - 2by + ay (x + y)(a - 2b) O F L I
FOIL is the order we use to multiply these expressions O
- 2bx
O:outer times outer F ax
F:first times first
(x + y)(a - 2b) L
- 2by
L: last times last I
+ ay
I:Inner times Inner
It is customary to write the letters (variables) in each term in alphabetical order and to write the number (coefficient) in front.

7. + 4x 2x2 + 3x + 6 (2x + 3)(x + 2) Answer: 2x2 + 7x + 6 O F L I
O:outer times outer F
2x2
F:first times first
(2x + 3)(x + 2) I
+ 3x
I:Inner times Inner L
+ 6
L: last times last
Very often the two middle terms are “like terms” and
can be combined. 4x + 3x = 7x
Answer: 2x2 + 7x + 6

8. + 3x 6x2 - 8x - 4 (3x - 4)(2x + 1) Answer: 6x2 - 5x - 4 O F L I
O:outer times outer F
6x2
F:first times first
(3x - 4)(2x + 1) I
- 8x
I:Inner times Inner L
- 4
L: last times last
Very often the two middle terms are “like terms” and
can be combined. 3x - 8x = -5x
Answer: 6x2 - 5x - 4

9. + 6x x2 - 6x - 36 (x - 6) (x + 6) Answer: x2 - 36 O F L I
O:outer times outer F x2
F:first times first
(x - 6) (x + 6) I
- 6x
I:Inner times Inner L
- 36
L: last times last
The answer to this kind of problem is called
“the difference of two squares”
The middle term always cancels out (6x – 6x = 0)
Answer: x2 - 36

10. FOIL Practice Problems: (Hit enter to see the answers)
(x + 7)(x – 3)
(x – 2)(x – 5)
3) (x + 2y)(3x + y)
(x + 3)(x – 3)
(2 + x)(3 + x)
Answers:
1) x2 + 4x – 21
2) x2 – 7x + 10
3) 3x2 + 7xy + 2y2
4) x2 - 9
5) 6 + 5x + x2

11. Questions? send e-mail to: lgreene1@satx.rr.com
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